Proton and Valence Quark Charge Radii for a Quasi-potential Model

Abstract

The problem of calculating the root-mean-square radius of proton charge distribution is studied for a relativistic quasi-potential quark model in the approximation of the SU(6) symmetry. It is demonstrated that in the case of point quarks, the proton radius is f(m/λ)/M², where m is the quark mass, λ is the binding energy scale parameter, M is the proton mass, and f is a dimensionless function independent of M. It is demonstrated that the root-mean-square radius of the coupled system can take a negative value in the ultrarelativistic range. For a joint description of the nucleon magnetic moments and of the proton radius, a negative root-mean-square quark radius, whose absolute value depends on the quark mass as 〈r ²_1q 〉 = −1.875 m², must be introduced into the model with oscillator forces.